I think doughnuts are meant to have the hole in the middle--it helps them cook evenly without having a soggy center. However, if you watch them carefully, you can cook holeless doughnuts, and then you can be really fancy and put jelly or pudding in the middle!
Jelly-filled doughnuts are a traditional Hanukkah treat. This is certainly not an authentic suvgani'ot recipe, but it's still a jelly-filled doughnut, and they're pretty good. ☺
spudnuts, but just cut round doughnuts--do not cut out the middles!
If you have an icing bag with a long tip, that would make things simple (just use it to pump jelly or pudding right to the center of the doughnut, with hardly a hole to the outside!)... BUT if you are like most of us and just have standard kitchen equipment, then take a knife and cut a small slit into the side of the doughnut and to the center.
Voila! Jelly filled doughnuts!